Let an integer be bad if there is no way to insert a colon among the digits of to form a time of day (on a twelve-hour, digital clock), and good if a colon can be inserted to form a time. For example, 100 is good because we can write 1:00, but 164 is bad. How many bad integers between 100 and 200 are equivalent to 3 mod 4?

supermanaccz
Apr 27, 2018

#1**+3 **

Hi supermanaccz!

So from 100 to 200, we first need to determine what numbers are bad.

From 100 to 159, they are all good, since we can have 1:00 and 1:59.

But from 160 to 199, they are all bad. There is no 1:60, since that will be 2 o'clock.

There is no 1: 99.

So we need to calculate how many numbers from 160 - 199 are equal to 3 mod 4.

The smallest number that is from 160 - 199 that is equal to 3 mod 4 is 163.

3 / 4 = 0 R 3

163 / 4 = 40 R 3

The largest is 199.

199 / 4 = 49 R 3

To calculate how many numbers we want from 163 to 199, we do:

\((199-163)/3+1=\boxed{13}\)

That will be your final answer .

I hope this helped,

gavin.

GYanggg
Apr 27, 2018